Given that the limit as h approaches 0 of (f(6 + h) - f(6))/h = -2, which of these statements must be true?

1. f'(6) exists
2. f(x) is continuous at x=6
3. f(6) < 0

4 answers

that is the very definition of the derivative of f(x) at x = 6
so
it exists, it is -2
the function is contiuous because it has a unique slope at 6
All I know is that the SLOPE is negative 2 at x = 6. I do NOT KNOW if the function is +, - or 0
Isn't #2 also supposed to be true? I thought f(x) had to be continuous at the point at which we find the derivative.
I agree :)
I suppose you could have the function jump up or down at x = 6 and have the same slope of -6 on both sides of the jump, but that is a bit of a stretch.
Similar Questions
  1. The limit as x approaches infinity. (1)/(5^x)The limit as x approaches 1. (1-x^3)/(2-sqrt(x^2-3)) Show your work thanks in
    1. answers icon 3 answers
  2. The table below gives selected values of a twice differentiable function f(x)x|. -7. -6. -4. -2. f(x)|. 0. -1. -2. 0 f'(x)|. 3.
    1. answers icon 1 answer
  3. Determine the behavior of limitsA. Limit as x approaches 1 of: (log x)/((x-1)^2) B. Limit as x approaches infinity of:
    1. answers icon 1 answer
    1. answers icon 0 answers
more similar questions